Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 5 - Section 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 288: 11


$= (2-\sqrt(3))$

Work Step by Step

$tan(15) = tan(60-45)$ $= \frac{[tan(60)-tan(45)]}{[1+tan(60)\times tan(45)]}$ $=\frac{[\sqrt(3)-1]}{[1+\sqrt(3)*1]}$ Multiply numerator and denominator by $(1-\sqrt(3))$ to get $= [-(1-\sqrt(3))^2]/(1-3)$ $= (1-2\sqrt(3)+3)/2$ $= (4-2\sqrt(3))/2$ $= (2-\sqrt(3))$
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